An empirical evaluation of fat-tailed distributions in modeling financial time series

There is substantial evidence that many financial time series exhibit leptokurtosis and volatility clustering. We compare the two most commonly used statistical distributions in empirical analysis to capture these features: the t distribution and the generalized error distribution (GED). A Bayesian approach using a reversible-jump Markov chain Monte Carlo method and a forecasting evaluation method are adopted for the comparison. In the Bayesian evaluation of eight daily market returns, we find that the fitted t error distribution outperforms the GED. In terms of volatility forecasting, models with t innovations also demonstrate superior out-of-sample performance.     

An empirical evaluation of kernels for time series

There exist a variety of distance measures which operate on time series kernels. The objective of this article is to compare those distance measures in a support vector machine setting. A support vector machine is a state-of-the-art classifier for static (non-time series) datasets and usually outperforms k-Nearest Neighbour, however it is often noted that that 1-NN DTW is a robust baseline for time-series classification. Through a collection of experiments we determine that the most effective distance measure is Dynamic Time Warping and the most effective classifier is kNN. However, a surprising result is that the pairing of kNN and DTW is not the most effective model. Instead we have discovered via experimentation that Dynamic Time Warping paired with the Gaussian Support Vector Machine is the most accurate time series classifier. Finally, with good reason we recommend a slightly inferior (in terms of accuracy) model Time Warp Edit Distance paired with the Gaussian Support Vector Machine as it has a better theoretical basis. We also discuss the reduction in computational cost achieved by using a Support Vector Machine, finding that the Negative Kernel paired with the Dynamic Time Warping distance produces the greatest reduction in computational cost.

     

Reducing error in neural network time series forecasting

Neural network time series forecasting error comprises autocorrelation error, due to an imperfect model, and random noise, inherent in the data. Both problems are addressed here, the first using a two stage training, growth-network neuron: the autocorrelation error (ACE) neuron. The second is considered as a post-processing noise filtering problem. These techniques are applied in forecasting the sunspot time series, with comparison of stochastic, BFGS and conjugate gradient solvers.     

An efficient time series forecasting model based on fuzzy time series

In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.     

A hybrid optimized error correction system for time series forecasting

Time series forecasting is a challenging task in machine learning. Real world time series are often composed by linear and nonlinear structures which need to be mapped by some forecasting method. Linear methods such as autoregressive integrated moving average (ARIMA) and nonlinear methods such as artificial neural networks (ANNs) could be employed to handle such problems, however model misspecification hinders the forecasting process producing inaccurate models. Hybrid models based on error forecasting and combination can reduce the misspecification of single models and improve the accuracy of the system. This work proposes a hybrid system that is composed of three parts: a) linear modeling of the time series, b) nonlinear modeling of the error series, and c) combination of the forecasts using three distinct approaches. The system performs a search for the best parameters of the linear and nonlinear components, and of the combination approaches. Particle swarm optimization is used to find suitable architecture and weights. Experiments show that the proposed technique achieved promising results in time series forecasting.     

An integrated fuzzy time series forecasting system

A number of fuzzy time series models have been designed and developed during the last decade. One problem of these models is that they only provide a single-point forecasted value just like the output of the crisp time series methods. In addition, these models are suitable for forecasting stationary or trend time series, but they are not appropriate for forecasting seasonal time series. Hence, the objective of this study is to develop an integrated fuzzy time series forecasting system in which the forecasted value will be a trapezoidal fuzzy number instead of a single-point value. Furthermore, this system can effectively deal with stationary, trend, and seasonal time series and increase the forecasting accuracy. Two numerical data sets are selected to illustrate the proposed method and compare the forecasting accuracy with four fuzzy time series methods. The results of the comparison show that our system can produce more precise forecasted values than those of four methods.     

Evaluating time series forecasting models: an empirical study on performance estimation methods

Machine Learning - Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. This process is a fundamental stage in any machine learning project. In this...     

间歇性时间序列的可预测性评估及联合预测方法

在高端制造企业的运维业务中,配件需求随机发生,且伴随有大量的零需求阶段,同时,对应的配件需求数据量小,且呈现出间歇性和块状分布的特点,导致现有时间序列预测方法难以有效预测配件需求走势。为解决该问题,提出了一种间歇性时间序列的可预测性评估及联合预测方法。首先,提出了一种新的间歇相似度指标,通过统计两条序列中“0”元素出现的频次和位置,并结合最大信息系数和平均需求间隔等度量指标,有效评估了序列的趋势信息和波动规律,并实现了对间歇性序列可预测性的量化;其次,基于该指标,构建了一个间歇相似度层次聚类方法来自适应地筛选相似性高、可预测性强的序列,剔除极度稀疏、无法预测的序列;此外,探索利用序列间的结构化信息,并构建多输出支持向量回归（M-SVR）模型,从而实现小样本下的间歇性序列联合预测;最后,分别在两个公开数据集（UCI礼品零售数据集和华为电脑配件数据集）和某大型制造企业实际配件售后数据集上进行实验。实验结果表明,相比多个典型的时间序列预测方法,所提方法可有效挖掘各类间歇性序列的可预测性,提高小样本间歇性序列的预测精度,从而为制造企业配件需求预测提供了一种新的解决方案。     

Handling forecasting problems based on fuzzy time series model and model error learning

Classical fuzzy time series forecasts are comprised of three steps: fuzzification, identification of fuzzy relation, and defuzzification. In this paper, we propose a new approach and add an error learning step to improve forecasts. In the fuzzification step, a hybrid method, based on the fuzzy c-means clustering and the fuzzy Silhouette criterion, is employed to determine the optimal number of intervals, which avoids time-consuming iterations of the whole algorithm. In the defuzzification step, an optimization model is set up to explain the rule of defuzzification. In the model structure, an error term is assembled into the traditional model to express model error, which is predicted by linear fitting and abnormal errors processing. Learning of model errors and considering of data characteristics guarantee good interpretability and accuracy. The numerical results show that the proposed approach has superior forecast performance to existing methods.     

Toward the development of a conventional time series based web error forecasting framework

Web reliability is gaining importance with time due to the exponential increase in the popularity of different social community networks, mailing systems and other online applications. Hence, to enhance the reliability of any existing web system, the web administrators must have the knowledge of various web errors present in the system, influences of various workload characteristics on the manifestation of several web errors and the relations among different workload characteristics. But in reality, often it may not be possible to institute a generalized correspondence among several workload characteristics. Moreover, the issues like the prediction and estimation of the cumulative occurrences of the source content failures and the corresponding time between failures of a web system become less highlighted by the reliability research community. Hence, in this work, the authors have presented a well-defined procedure (a forecasting framework) for the web admins to analyze and enhance the reliability of the web sites under their supervision. Initially, it takes the HTTP access and the error logs to extract all the necessary information related to the workloads, web errors and corresponding time between failures. Next, we have performed the principal component analysis, correlation analysis and the change point analysis to select the number of independent variables. Next, we have developed various time series based forecasting models for foretelling the cumulative occurrences of the source content failures and the corresponding time between failures. In the current work, the multivariate models also include various uncorrelated workloads, the exogeneous and the endogenous noises for forecasting the web errors and the corresponding time between failures. The proposed methodology has been validated with usage statistics collected from the web sites belong of two highly renowned Indian academic institutions.     

An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting

This paper compares the predictive performance of ARIMA, artificial neural network and the linear combination models for forecasting wheat price in Chinese market. Empirical results show that the combined model can improve the forecasting performance significantly in contrast with its counterparts in terms of the error evaluation measurements. However, as far as turning points and profit criterions are concerned, the ANN model is best as well as at capturing a significant number of turning points. The results are conflicting when implementing dissimilar forecasting criteria (the quantitative and the turning points measurements) to evaluate the performance of three models. The ANN model is overall the best model, and can be used as an alternative method to model Chinese future food grain price.     

Granger 相关性与时间序列预测

提出一种将Granger相关信息用于时间序列预测的方法,以解决时间序列预测过程中信息利用不完全的问题.首先,通过Granger相关性检验确定时间序列系统中的可利用信息;然后,利用神经网络将可利用信息抽取出来;最后,将抽取的可利用信息融入到时间序列的预测中.实验结果验证了所提出预测方法的有效性和稳定性.     

A comparison of time series and machine learning models for inflation forecasting: empirical evidence from the USA

This study compares time series and machine learning models for inflation forecasting. Empirical evidence from the USA between 1984 and 2014 suggests that out of sixteen conditions (four different inflation indicators and four different horizons), machine learning models provide more accurate forecasting results in seven conditions and the time series models are better in nine conditions. Moreover, multivariate models give better results in fourteen conditions, and univariate models are better only in two conditions. This study shows that machine learning model prevails against time series models for the core personal consumption expenditure (core-PCE) inflation forecasting, and the time series model (ARDL) is better for the core consumer price (core-CPI) index inflation forecasting in all horizons.

     

A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting

Time series forecasting is an important and widely popular topic in the research of system modeling, and stock index forecasting is an important issue in time series forecasting. Accurate stock price forecasting is a challenging task in predicting financial time series. Time series methods have been applied successfully to forecasting models in many domains, including the stock market. Unfortunately, there are 3 major drawbacks of using time series methods for the stock market: (1) some models can not be applied to datasets that do not follow statistical assumptions; (2) most time series models that use stock data with a significant amount of noise involutedly (caused by changes in market conditions and environments) have worse forecasting performance; and (3) the rules that are mined from artificial neural networks (ANNs) are not easily understandable.To address these problems and improve the forecasting performance of time series models, this paper proposes a hybrid time series adaptive network-based fuzzy inference system (ANFIS) model that is centered around empirical mode decomposition (EMD) to forecast stock prices in the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Hang Seng Stock Index (HSI). To measure its forecasting performance, the proposed model is compared with Chen's model, Yu's model, the autoregressive (AR) model, the ANFIS model, and the support vector regression (SVR) model. The results show that our model is superior to the other models, based on root mean squared error (RMSE) values.     

Eye-tracking for user modeling in exploratory learning environments: An empirical evaluation

In this paper, we describe research on using eye-tracking data for on-line assessment of user meta-cognitive behavior during interaction with an environment for exploration-based learning. This work contributes to user modeling and intelligent interfaces research by extending existing research on eye-tracking in HCI to on-line capturing of high-level user mental states for real-time interaction tailoring. We first describe the empirical work we did to understand the user meta-cognitive behaviors to be modeled. We then illustrate the probabilistic user model we designed to capture these behaviors with the help of on-line information on user attention patterns derived from eye-tracking data. Next, we describe the evaluation of this model, showing that gaze-tracking data can significantly improve model performance compared to lower level, time-based evidence. Finally, we discuss work we have done on using pupil dilation information, also gathered through eye-tracking data, to further improve model accuracy.     

Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks

Neural networks have been widely used for short-term, and to a lesser degree medium and long-term, demand forecasting. In the majority of cases for the latter two applications, multivariate modeling was adopted, where the demand time series is related to other weather, socio-economic and demographic time series. Disadvantages of this approach include the fact that influential exogenous factors are difficult to determine, and accurate data for them may not be readily available. This paper uses univariate modeling of the monthly demand time series based only on data for 6 years to forecast the demand for the seventh year. Both neural and abductive networks were used for modeling, and their performance was compared. A simple technique is described for removing the upward growth trend prior to modeling the demand time series to avoid problems associated with extrapolating beyond the data range used for training. Two modeling approaches were investigated and compared: iteratively using a single next-month forecaster, and employing 12 dedicated models to forecast the 12 individual months directly. Results indicate better performance by the first approach, with mean percentage error (MAPE) of the order of 3% for abductive networks. Performance is superior to naı¨ve forecasts based on persistence and seasonality, and is better than results quoted in the literature for several similar applications using multivariate abductive modeling, multiple regression, and univariate ARIMA analysis. Automatic selection of only the most relevant model inputs by the abductive learning algorithm provides better insight into the modeled process and allows constructing simpler neural network models with reduced data dimensionality and improved forecasting performance.     

Setting forecasting model parameters using unconstrained direct search methods: An empirical evaluation

Exponential smoothing (ES) forecasting models represent an important tool that conjugates compactness, ease of implementation, and robustness. The parameterization (i.e., the determination of the parameters) of an ES model can be represented as a (non-linear) minimization problem. A solution to the problem consists of the ES model’s parameter values that minimize the forecast error. Nonetheless, the task of solving such a minimization problem represents a challenge in that it should balance the accuracy of the resulting forecasts and the computational time required, especially when the parameterization concerns hundreds of time series and models. Therefore, in this paper, we discuss the empirical performance of two derivative free search methods for solving the minimization problem, and compare them with other, well-assessed search procedures. In doing so, we propose an adaptation of the general exponential smoothing model to handle box-constraints on parameter values. In the computational experiments, the derivative free methods displayed a performance similar to that of a gradient-based method, requiring only a fraction of the computation effort.     

Noise reduction of NDVI time series: An empirical comparison of selected techniques

Satellite-derived NDVI time series are fundamental to the remote sensing of vegetation phenology, but their application is hindered by prevalent noise resulting chiefly from varying atmospheric conditions and sun-sensor-surface viewing geometries. A model-based empirical comparison of six selected NDVI time series noise-reduction techniques revealed the general superiority of the double logistic and asymmetric Gaussian function-fitting methods over four alternative filtering techniques. However, further analysis demonstrated the strong influence of noise level, strength, and bias, and the extraction of phenological variables on technique performance. Users are strongly cautioned to consider both their ultimate objectives and the nature of the noise present in an NDVI data set when selecting an approach to noise reduction, particularly when deriving phenological variables.     

Integration of multi-time-scale models in time series forecasting

A solution to the problem of producing long-range forecasts on a short sampling interval is proposed. It involves the incorporation of information from a long sampling interval series, which could come from an independent source, into forecasts produced by a state-space model based on a short sampling interval. The solution is motivated by the desire to incorporate yearly electricity consumption information into weekly electricity consumption forecasts. The weekly electricity consumption forecasts are produced by a state-space structural time series model. It is shown that the forecasts produced by the forecasting model based on weekly data can be improved by the incorporation of longer-time-scale information, particularly when the forecast horizon is increased from 1 year to 3 years. A further example is used to demonstrate the approach, where yearly UK primary fuel consumption information is incorporated into quarterly fuel consumption forecasts.     

Distribution forecasting of high frequency time series

The availability of high frequency data sets in finance has allowed the use of very data intensive techniques using large data sets in forecasting. An algorithm requiring fast k-NN type search has been implemented using AURA, a binary neural network based upon Correlation Matrix Memories. This work has also constructed probability distribution forecasts, the volume of data allowing this to be done in a nonparametric manner. In assistance to standard statistical error measures the implementation of simulations has allowed actual measures of profit to be calculated.